Arrays

An array a with elements of type A is declared as:

a:A[_];

Multidimensional arrays, with any number of dimensions, are declared as:

b:B[_,_];    // two-dimensional array
c:C[_,_,_];  // three-dimensional array, etc

The rightmost dimension is the innermost (fastest moving) in the memory layout. Two-dimensional arrays that represent matrices are therefore in row-major order.

The size of the array may be given in the square brackets when it is declared, in place of _:

a:A[4];
b:B[4,8];

Alternatively, arrays can be initialized using a sequence of element values in square brackets:

a:Real[_] <- [0.0, 1.0, 2.0];

It is possible to nest these sequences to construct higher-dimensional arrays:

A:Real[_,_] <- [[1.0, 0.0], [0.0, 1.0]];

Arrays are sliced with square brackets. To select the element of b at row 2 and column 6, use:

b[2,6]

This returns a single element of type B. To select the range of elements of b at row 2 and columns 5 to 8, use:

b[2,5..8]

This returns a vector of type B[_].

In the context of array slicing, the term index denotes a single index, as in 2 and 6 above; while the term range denotes a pair of indices separated by .., as in 5..8 above.

Indices reduce the number of dimensions in the result; they do not create singleton dimensions. Revisiting the previous example for emphasis, the result is of type B[_] with size 4, not of type B[_,_] with size 1 by 4. When a singleton dimension is desired, use a singleton range that starts and ends at the same index:

b[2..2,5..8]

Arrays are resized by assignment, e.g.

a:A[4];
d:A[2];
d <- a;

The vector d is now a copy of a, with size 4. Its previous value is discarded.

When slicing an array on the left side of an assignment, suggesting a view of the existing array, sizes must match on the left and right:

d[1..2] <- a[1..2];  // OK! Both left and right have size 2
d[1..2] <- a;        // ERROR! Left has size 2, right has size 4

Assignment may be used to resize an array, but not to change its number of dimensions. The number of dimensions of an array is a fundamental part of its type.

Sequences can be assigned to arrays:

x <- [a, b, c];
x <- [[a, b, c], [d, e, f]];

But arrays cannot be assigned to sequences, as sequences are read-only.